The general covariance can be recovered by Stueckelberging the mini superspace action [1]}. We may follow the following dictionary,
\(\frac{1}{a^2}\rightarrow \frac{1}{3}g^{ij}\delta _{ij}\rightarrow g^{\mu \nu }\partial _\mu \phi ^a\partial _\nu \phi ^b\delta _{ab}, &&\qquad \text{where}\qquad \langle \phi ^a\rangle =\frac{x^i\delta _{ia}}{\sqrt{3}},\nonumber \\L\rightarrow \varphi (t,\textbf {x}), \nonumber \\-\frac{\dot{L}^2}{N^2}\rightarrow g^{\mu \nu }\partial _\mu \varphi \partial _\nu \varphi ,&&\qquad \text{where}\qquad \langle \varphi \rangle =\varphi (t),\) 
